16.2 Entropy  (Page 5/8)

In [link] all possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, Δ S , if the particles are initially evenly distributed between the two boxes, but upon redistribution all end up in Box (b).

In [link] all of the possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, Δ S , for the system when it is converted from distribution (b) to distribution (d).

How does the process described in the previous item relate to the system shown in [link] ?

Consider a system similar to the one in [link] , except that it contains six particles instead of four. What is the probability of having all the particles in only one of the two boxes in the case? Compare this with the similar probability for the system of four particles that we have derived to be equal to $\frac{1}{8}.$ What does this comparison tell us about even larger systems?

Consider the system shown in [link] . What is the change in entropy for the process where the energy is initially associated only with particle A, but in the final state the energy is distributed between two different particles?

Consider the system shown in [link] . What is the change in entropy for the process where the energy is initially associated with particles A and B, and the energy is distributed between two particles in different boxes (one in A-B, the other in C-D)?

Arrange the following sets of systems in order of increasing entropy. Assume one mole of each substance and the same temperature for each member of a set.

(a) H ₂ ( g ), HBrO ₄ ( g ), HBr( g )

(b) H ₂ O( l ), H ₂ O( g ), H ₂ O( s )

(c) He( g ), Cl ₂ ( g ), P ₄ ( g )

At room temperature, the entropy of the halogens increases from I ₂ to Br ₂ to Cl ₂ . Explain.

Consider two processes: sublimation of I ₂ ( s ) and melting of I ₂ ( s ) (Note: the latter process can occur at the same temperature but somewhat higher pressure).

${\text{I}}_2(s)⟶{\text{I}}_2(g)$

${\text{I}}_2(s)⟶{\text{I}}_2(l)$

Is Δ S positive or negative in these processes? In which of the processes will the magnitude of the entropy change be greater?

Indicate which substance in the given pairs has the higher entropy value. Explain your choices.

(a) C ₂ H ₅ OH( l ) or C ₃ H ₇ OH( l )

(b) C ₂ H ₅ OH( l ) or C ₂ H ₅ OH( g )

(c) 2H( g ) or H( g )

Predict the sign of the entropy change for the following processes.

(a) An ice cube is warmed to near its melting point.

(b) Exhaled breath forms fog on a cold morning.

(c) Snow melts.

Predict the sign of the entropy change for the following processes. Give a reason for your prediction.

(a) ${\text{Pb}}^{\mathrm{2+}}(aq)+{\text{S}}^{\mathrm{2-}}(aq)⟶\text{PbS}(s)$

(b) $2\text{Fe}(s)+3{\text{O}}_2(g)⟶{\text{Fe}}_2{\text{O}}_3(s)$

(c) $2{\text{C}}_6{\text{H}}_{14}(l)+19{\text{O}}_2(g)⟶14{\text{H}}_2\text{O}(g)+12{\text{CO}}_2(g)$

Write the balanced chemical equation for the combustion of methane, CH ₄ ( g ), to give carbon dioxide and water vapor. Explain why it is difficult to predict whether Δ S is positive or negative for this chemical reaction.

Write the balanced chemical equation for the combustion of benzene, C ₆ H ₆ ( l ), to give carbon dioxide and water vapor. Would you expect Δ S to be positive or negative in this process?